Ichikawa's wiki

**以前のリビジョンの文書です** ----

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====== 統計についてメモ ====== ===== Covariance Matrix ===== $ X=\pmatrix{ X_1\\ X_2\\ .\\ .\\ .\\ X_n\\} $is a set of observables. Covariance matrix is defined as <jsmath> \Sigma = \pmatrix{ <(X_1-\mu_1)(X_1-\mu_1)> & & <(X_1-\mu_1)(X_2-\mu_2)> & ... & <(X_1-\mu_1)(X_n-\mu_n)> & \\ <(X_2-\mu_2)(X_1-\mu_1)> & & <(X_2-\mu_2)(X_2-\mu_2)> & ... & <(X_2-\mu_2)(X_n-\mu_n)> & \\ .\\ .\\ .\\ <(X_n-\mu_n)(X_1-\mu_1)> & & <(X_n-\mu_n)(X_2-\mu_2)> & ... & <(X_n-\mu_n)(X_n-\mu_n)> & \\ } </jsmath>\\ Note: diagonal term is equal to $\sigma_i^2$. $\Sigma_{ij}>0$ : positive correlation.\\ $\Sigma_{ij}=0$ : no correlation.\\ $\Sigma_{ij}<0$ : negative correlation.\\